Quotes About Mathematics

The first and foremost duty of the high school in teaching mathematics is to emphasize methodical work in problem solving...The teacher who wishes to serve equally all his students, future users and nonusers of mathematics, should teach problem solving so that it is about one-third mathematics and two-thirds common sense.

Like a stool which needs three legs to be stable, mathematics education needs three components: good problems, with many of them being multi-step ones, a lot of technical skill, and then a broader view which contains the abstract nature of mathematics and proofs. One does not get all of these at once, but a good mathematics program has them as goals and makes incremental steps toward them at all levels.

People think that mathematics is complicated. Mathematics is the simple bit, it’s the stuff we CAN understand. It’s cats that are complicated.

The mathematics is the odd one, odd because I'm not sure how to measure its effect. It is so fundamental to my outlook on everything and yet I'm not even sure how. It must be because in my formative years it was everything to me, the single place of beauty in my life, and of breathtaking beauty at that. I still believe that pure mathematics is the most creative thing that humanity does, though I am no longer a part of it.

Is mathematics doomed to suffer the same fate as other sciences that have split into separate branches?... Mathematics is, in my opinion, an indivisible whole... May the new century bring with it ingenious champions and many zealous and enthusiastic disciples.

For me, rhythm is a type of divine mathematics in a way. No matter where you're from, we can all understand the mathematics of rhythm. I try to apply this mathematical thinking to my playing.

On all levels primary, and secondary and undergraduate - mathematics is taught as an isolated subject with few, if any, ties to the real world. To students, mathematics appears to deal almost entirely with things whlch are of no concern at all to man.

Mathematics is so much easier than words mathematics makes things clear that words merely muddle and confuse and mess up.

To exist (in mathematics), said Henri Poincaré, is to be free from contradiction. But mere existence does not guarantee survival. To survive in mathematics requires a kind of vitality that cannot be described in purely logical terms.

The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.

In mathematics I can report no deficiency, except it be that men do not sufficiently understand the excellent use of Pure Mathematics.

A Noah's Ark of mathematicians, their lives, loves, hard times, and madnesses, Loving and Hating Mathematics shows our community with all its warts as well as its triumphs. I especially liked the chapter on much-hated school mathematics, 'Almost All Children Left Behind.'

Mathematical economics is old enough to be respectable, but not all economists respect it. It has powerful supporters and impressive testimonials, yet many capable economists deny that mathematics, except as a shorthand or expository device, can be applied to economic reasoning. There have even been rumors that mathematics is used in economics (and in other social sciences) either for the deliberate purpose of mystification or to confer dignity upon common places as French was once used in diplomatic communications.

Given the brief - and generally misleading - exposure most people have to mathematics at school, raising the public awareness of mathematics will always be an uphill battle.

Mathematics is a language plus reasoning. It's like a language plus logic. Mathematics is a tool for reasoning.

The mathematics clearly called for a set of underlying elementary objects-at that time we needed three types of them-elementary objects that could be combined three at a time in different ways to make all the heavy particles we knew. ... I needed a name for them and called them quarks, after the taunting cry of the gulls, "Three quarks for Muster mark," from Finnegan's Wake by the Irish writer James Joyce.

Mathematics is the handwriting on the human consciousness of the very Spirit of Life itself.

Strange as it may sound, the power of mathematics rests on its evasion of all unnecessary thought and on its wonderful saving of mental operations.

Mathematics is a dangerous profession; an appreciable proportion of us go mad.

Beauty means a lot of different things to a lot of different people. A lot of different ways in which things can be beautiful. But this really has a very specific meaning and which is more along the lines of elegance which is that we say an idea is beautiful or elegant in mathematics or physics if a very simple principle or a very simple idea, or simple set of ideas, turns out to be very powerful and leads to all sort of unexpected structure and unexpected predictions.

In mathematics, two angles that are said to coincide fit together perfectly. The word "coincidence" does not describe luck or mistakes. It describes that which fits together perfectly.

Mathematics is not yet capable of coping with the naïveté of the mathematician himself.

What would mathematics have amounted to without the imagination of its devotees-its giants and their followers? There never was a discovery made without the urge of imagination-of imagination which broke the roadway through the forest in order that cold logic might follow.

... You get surreal numbers by playing games. I used to feel guilty in Cambridge that I spent all day playing games, while I was supposed to be doing mathematics. Then, when I discovered surreal numbers, I realized that playing games IS math.

These days people are much more aware that mathematics is a communal endeavor: even the most brilliant idea gets meaning only from its relation to the whole.

It becomes the urgent duty of mathematicians, therefore, to meditate about the essence of mathematics, its motivations and goals and the ideas that must bind divergent interests together.

What humans do with the language of mathematics is to describe patterns.

[Mathematics] is an independent world created out of pure intelligence.

Poetry is a mystic, sensuous mathematics of fire, smoke-stacks, waffles, pansies, people, and purple sunsets.

Increasingly, the mathematics will demand the courage to face its implications.

Thinking - in particular abstract thinking, which most of us are introduced to through the study of mathematics and literature - helps us learn that we can become problem solvers.

In no other branch of mathematics is it so easy for experts to blunder as in probability theory.

I have a true aversion to teaching. The perennial business of a professor of mathematics is only to teach the ABC of his science; most of the few pupils who go a step further, and usually to keep the metaphor, remain in the process of gathering information, become only Halbwisser [one who has superficial knowledge of the subject], for the rarer talents do not want to have themselves educated by lecture courses, but train themselves. And with this thankless work the professor loses his precious time.

The mathematics is not there till we put it there.

Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose.

Proofs exist only in mathematics and logic, not in science.

This is not mathematics; this is theology.

The desire to explore thus marks out the mathematician. This is one of the forces making for the growth of mathematics. The mathematician enjoys what he already knows; he is eager for more knowledge.

Mathematics is the gate and key to science.

Mathematics - the unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to human affairs.

Mathematics would certainly have not come into existence if one had known from the beginning that there was in nature no exactly straight line, no actual circle, no absolute magnitude.

I think the biggest misconception is that everybody has to learn mathematics. That seems to be a complete mistake.

If I had to design a mechanism for the express purpose of destroying a child's natural curiosity and love of pattern-making, I couldn't possibly do as good a job as is currently being done-I simply wouldn't have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.

Mathematics - this may surprise or shock some - is never deductive in creation.

The bottom line for mathematicians is that the architecture has to be right. In all the mathematics that I did, the essential point was to find the right architecture. It's like building a bridge. Once the main lines of the structure are right, then the details miraculously fit. The problem is the overall design.

By and large it is uniformly true in mathematics that there is a time lapse between a mathematical discovery and the moment when it is useful; and that this lapse of time can be anything from 30 to 100 years, in some cases even more; and that the whole system seems to function without any direction, without any reference to usefulness, and without any desire to do things which are useful.

Man is full of desires: he loves only those who can satisfy them all. "This man is a good mathematician," someone will say. But I have no concern for mathematics; he would take me for a proposition. "That one is a good soldier." He would take me for a besieged town. I need, that is to say, a decent man who can accommodate himself to all my desires in a general sort of way.

And as for Mixed Mathematics, I may only make this prediction, that there cannot fail to be more kinds of them, as nature grows further disclosed.